Three frequency modulated combination thermal neutron lifetime log and porosity

ABSTRACT

Methods are disclosed for measuring simultaneously the thermal neutron lifetime of the borehole fluid and earth formations in the vicinity of a well borehole, together with the formation porosity. A harmonically intensity modulated source of fast neutrons is used to irradiate the earth formations with fast neutrons at three different intensity modulation frequencies. Intensity modulated clouds of thermal neutrons at each of the three modulation frequencies are detected by dual spaced detectors and the relative phase shift of the thermal neutrons with respect to the fast neutrons is determined at each of the three modulation frequencies at each detector. These measurements are then combined to determine simultaneously the thermal neutron decay time of the borehole fluid, the thermal neutron decay time of surrounding earth formation media and the porosity of the formation media.

This application is a continuation-in-part of copending application Ser. No. 489,330, filed July 17, 1974.

BACKGROUND OF THE INVENTION

This invention relates to in situ measurements of earth formations traversed by a well borehole. In particular the invention relates to the measurement of the thermal neutron lifetime or thermal neutron decay time and the porosity of earth formations in the vicinity of a well bore.

The techniques used in the present invention include the generation as a function of time of a phase coherent intensity modulated cloud of fast neutrons in a well bore which results in the creation of a phase coherent thermal neutron cloud being produced as the fast neutrons are slowed to thermal energy by the materials in the vicinity of the well bore. Measurements of the relative phase of the thermal neutron cloud population density with respect to the fast neutron cloud generated at each of dual spaced detectors lead to the determination of parameters relating to the thermal neutron decay time or neutron lifetime of the formations in the vicinity of the well bore and the borehole fluid itself, together with the formation porosity.

BRIEF DESCRIPTION OF THE PRIOR ART

At the present time there are two principal techniques used for measuring, in situ, the thermal neutron decay time or thermal neutron lifetime or earth formations in the vicinity of a well borehole. These neutron lifetime measurements have proven to be particularly valuable in evaluating earth formations in cased well boreholes. In both of these techniques a logging instrument which traverses the well bore uses a pulsed source of high energy of fast (14 MEV) neutrons.

In the first of these measurement techniques the neutron source is repetitively pulsed. For each fast neutron pulse, a cloud of fast neutrons is injected in a generally spherically symmetric fashion about the source to the surrounding earth formations. The fast neutron cloud passes from the well tool through the drilling mud, well bore casing, and cement between the casing and earth formations surrounding the well bore. Each such pulse of fast neutrons has approximately a constant intensity and lasts typically for a time duration of from 20 to 30 microseconds. This time lapse is generally adequate to create a thermalized (or low energy) neutron population in the earth formations and borehole. The number of thermal neutrons comprising this cloud or population then decays exponentially due to the capture of the thermalized neutrons by formation and borehole elemental nuclei.

After an initial time period, (about 300 microseconds) during which resultant gamma ray effects in the borehole, mud, and casing are substantially dissipated, measurements of the number of thermalized neutrons in the vicinity of the well tool are made during two successive time intervals and can be used to define an exponential decay curve for the thermal neutron population either in the borehole or the earth formation surrounding the borehole. Which of these two thermal neutron decay characteristics is being measured is not known with certainty due to the fact that the assumption is made in this measurement technique that the borehole thermal neutron decay time is substantially shorter and hence dies out quicker than that of the surrounding earth formations. This assumption that the borehole component of thermal neutron decay time (or thermal neutron lifetime) is generally shorter than the formation thermal neutron decay time or thermal neutron lifetime usually occurs while drilling fluids having a high chlorine content (or salt water content) are encountered. However, in boreholes containing air, gas, fresh water or oil this relationship does not always hold. One striking advantage of the present invention over this prior art thermal neutron lifetime measuring technique is that no assumption is made as to the relative thermal neutron decay characteristic of the borehole fluid or with respect to that of the formations surrounding the borehole. Accordingly, the present invention overcomes the aforementioned limitation of the prior art.

Measurements of the number of thermalized neutrons in the vicinity of the well tool during the successive time intervals following the initial time lapse to allow for die away of borehole effects can be used to define an exponential decay curve for the thermal neutron population of the earth formations in the vicinity of the borehole.

These two time intervals or time gates, for example, can be fixed between 400-600 microseconds following the neutron burst, and between 700-900 microseconds following the neutron burst in typical earth formations, and under borehole conditions wherein a saline fluid or high chlorine content salt is present in the borehole fluid.

If neutron diffusion effects are ignored, the relationship for the decay of a thermal neutron population in a homogeneous medium having a thermal neutron macroscopic capture cross-section ε can be expressed as:

    N.sub.2 = N.sub.1, e.sup.-.sup.ε.sup.vt            ( 1)

wherein N₁ is the number of thermal neutrons at a first point in time, t₁ ; N₂ is the number of thermal neutron at a later point in time, t₂ ; e is the Naperian logarithm base; t is the time between two measurements (t₂ -t₁); and v is the velocity of the thermal neutrons. The macroscopic thermal neutron capture cross section ε of a reservoir rock (which can be obtained from Equation (1) is dependent upon its porosity, the formation water salinity, and the quantity and type of petroleum contained in the pore spaces therein and thus is a valuable measurement to obtain.

When neutrons from the high energy neutron source interact with the materials in a well bore and with surrounding earth formations, they are slowed down and lose energy. A primary agent for slowing down neutrons is hydrogen which is relatively available in water and hydrocarbon. After the fast neutrons have been slowed they are captured by formation nuclei (primarily by chlorine) and, in general, will generate characteristic capture gamma rays before returning to a stable state. It is the capture gamma rays which are detected during the two different time inervals of this system of measuring thermal neutron decay time. The number of such gamma rays detected is proportional to the thermal neutron population in the vicinity of the well tool. Alternatively, thermal neutrons themselves can be detected during these intervals by the use of helium 3 or boron trifluoride detectors if desired. Thus, by the means of the two fixed time gating masurements the thermal neutron macroscopic capture cross section ε can be determined.

A second prior art technique for measuring thermal neutron decay time or thermal neutron lifetime uses the reciprocal of the macroscopic thermal neutron capture cross section ε which is defined in terms of τ (the time constant for absorption of the thermal neutrons). A relationship analogous to Equation (1), but defined in terms of τ is given by:

    N = N.sub.o e .sup.-.sup.t/.sup.τ                      ( 2)

where τ = 1/vε

Here N is thermal neutron density at any time t; N_(o) is the thermal neutron density at an initial time t_(o) ; e is the Naperian constant; τ is the time required for the thermal neutron population to decay to 1/e of its value at t_(o).

In measuring the thermal neutron decay time using this second prior art technique, the logging equipment obtains counts of capture gamma rays during two successive time intervals following the generation of the thermal neutron cloud in the vicinity of the well borehole to define the exponential decay curve. In this technique, however, the two time intervals of the measurement are defined as a function of the 96 actually measured during a previous measurement cycle. The value of τ previously measured is used to establish the neutron burst duration for the generation of the fast neutrons; the waiting interval to the opening to the first time gate, the duration of the first time gate, the duration of the time between the time gates and the duration of the second time gate. All of these times are related to τ as previously measured. This technique is commonly referred to in the art as the "sliding gate" technique. In a more recent version of this system, two gamma ray detectors spaced apart are used. By deriving the τ at each detector separately and then combining these measurements in a predetermined manner, an estimate of the porosity of the formation between the two spaced detectors may be obtained also.

Both of the foregoing systems of measurement have been successfully used to measure the decay time or lifetime of thermal neutrons as long as the borehole component of thermal neutron population dies away substantially faster than the formation component of the thermal neutron population in the vicinity of the borehole. Both of these techniques utilize a neutron burst of substantially constant intensity (a square wave neutron pulse).

BRIEF DESCRIPTION OF THE INVENTION

In the present invention a well logging tool is moved through the borehole and includes an intensity modulated fast neutron source and two gamma ray detectors (or, alternatively, two thermal neutron detectors). The neutron source generates a generally harmonically varying population of fast neutrons as a function of time. These neutrons are introduced into the media surrounding the well borehole and result in a thermal neutron population being generated from the slowing down of the fast neutrons in the media and borehole itself. This cloud of thermalized neutrons itself comprises a phase coherent intensity varying neutron population whose presence is detected as a function of time by the thermal neutron or gamma ray detectors at two different distances from the neutron source. The fast neutron source is harmonically or sinusoidally modulated at a plurality of frequencies. The relative phase angle of the phase coherent thermal neutron population which is generated at each of the modulation frequencies is detected by each of the detectors. This phase angle information contains components due to the effect of the borehole fluid and the media surrounding the borehole. Moreover, the measurements at the two detectors are influenced by the porosity of the earth formations. By appropriately combining these measurements made at the plurality of different modulation frequencies at the two detectors according to predetermined relationships, the thermal neutron lifetime (or thermal neutron decay time) of the borehole fluid and the media surrounding the well bore may be determined. Also the porosity of the media in the vicinity of the borehole may be obtained.

In practice, the measurements of the relative phase angles at each of the modulation frequencies are made by combining counts from each of the detectors in a particular manner to derive the value of the tangent of the phase angle. From this tangent information the formation thermal neutron decay time τ or the corresponding thermal neutron macroscopic capture cross section value ε can be established. By using this information in conjunction with a different combination of the count rate measurements, the formation porosity is determinable.

Electronic systems are provided in the downhole tool and at the surface for producing a sequence of different frequency intensity modulated fast neutron clouds operating at least at three different frequencies of operation. Synchronization (or sync) pulses are also generated and these provide a means for separating the counts of gamma rays representative of thermal neutrons during the portion of a measurement cycle corresponding to measurements made at each of the different frequencies of intensity modulation of the neutron source and from each of the dual spaced detectors. At the earth's surface the signal from each detector in the downhole tool are separated and counts are made as a function of time of the thermal neutron population in the vicinity of the tool at each of the three frequencies at each detector. These counts are used to determine the tangents of the relative phase angles between the thermal neutron populations and the source of fast neutrons at each of the frequencies at each detector. A recorder is provided for making a record of these measurements as a function of the borehole depth of the well tool. Moreover, the invention includes techniques for determining the value of the thermal neutron decay time τ and/or the macroscopic thermal neutron capture cross section ε of both the media surrounding the borehole and the borehole fluid together with formation porosity.

The invention is best understood by reference to the following detailed description thereof, when taken in conjunction with the accompanying drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an overall block diagram illustrating schematically the apparatus of the invention in a well borehole.

FIG. 2 is a circuit diagram showing the downhole portion of the system of the invention.

FIG. 3 is a circuit diagram showing the surface portion of the system of the invention.

FIGS. 4 and 4a are graphical representations showing the relationship between the phase angle tangents at two different modulation frequencies.

FIGS. 5 and 5a are graphical representations showing the relationship between the phase angle tangents at two different modulation frequencies.

FIG. 6 is a graphical representation showing the relationship between thermal neutron lifetime measured by phase angles measured at two different pairs of frequencies of modulation.

FIG. 7 is a schematic illustration of the waveform of signals sent to the surface from the downhole tool in the invention; and

FIG. 8 is a schematic illustration showing the measurement cycle or sequence of neutron outputs at three different frequencies of intensity modulation of the neutron source.

FIG. 9 is a graphical illustration showing the counting periods used to determine the relative phase shifts.

FIG. 10 is a graphical representation showing the formation porosity as a function of neutron slowing down length for several different formation lithology characteristics.

FIG. 11 is a graphical representation showing the ratio of borehole to formation amplitudes as measured at two different pairs of frequencies of modulation.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention contemplates making measurements of the intensity phase shift of a phase coherent thermal neutron population cloud with respect to the intensity modulated fast neutron population generated by a neutron source at three different intensity modulation frequencies at two different spaced detectors. By appropriately combining the measurements of the phase shift at each of the frequencies at each detector the thermal neutron lifetime (or decay time) of both the borehole component of the neutron flux and the formation component of the neutron flux may be determined. Also, the formation porosity may be simultaneously determined. No a priori knowledge of borehole conditions is necessary.

Referring initially to FIG. 1, a system in accordance with the concepts of the invention is illustrated schematically. A well borehole 10 traverses earth formations 11, and is lined with a tubular casing 12, which is cemented in place by cement layer 13. Suspended in the borehole 10 is a well logging sonde 14 which is suspended therein by an armored well logging cable 15. The cable 15 passes over a sheave wheel 16 which is electrically or mechanically linked (as indicated by the dotted line 17) to a recorder 18 of the type conventionally used in well logging. The record medium 19 of the recorder 18 may thus be driven as a function of the borehole depth of the well logging tool. The borehole 10 is filled with a fluid 20 which may be either a salt (saline) solution or fresh water or oil. The present invention works equally well in salt or fresh water environments or in air filled boreholes which is an advantage over prior art thermal neutron lifetime or decay time measuring systems which did not perform well in fresh water or oil filled boreholes.

The well logging sonde 14 used with the present invention contains a neutron generator 21, circuitry for driving the neutron generator 22, a first gamma ray detector 23 and a second gamma ray detector 26. Appropriate circuitry 24 for controlling the neutron generator 21 and for amplifying signals from the detectors 23 and 26 is also provided. A surface power supply 28 provides operative power for the downhole systems via the conductors of the well logging cable 15. Signals from the downhole tool are processed by surface data processing circuits 25 which will be described in more detail subsequently. Output signals from the data processing circuits 25 are supplied to the recorder 18 whose record medium 19 is driven as a function of depth as previously mentioned.

The gamma ray detectors 23 and 26 may be thallium activated sodium or cesium iodide crystals which are optically coupled to photomultiplier tubes. A control electronic section 24 provides signals, as will be subsequently described in more detail, to operate the neutron generator 21 and the photomultipliers and detectors 23 and 26. Radiation detected by the detectors 23 and 26 is presented for transmission to the surface as sharply peaked positive voltage pulses of different amplitude levels for detector 23 and as sharply peaked negative voltage pulses for detector 26 which will be described in more detail subsequently. These pulses are presented to the cable 15 conductors for transmission to the surface. Similarly, much larger amplitude sharp peaked synchronization (negative voltage) pulses are also supplied, as will be described in more detail subsequently, for transmission to the surface, on cable 15 conductors.

The neutron generator 21 is preferably of the deuterium-tritium accelerator type as known in the art. This type of neutron source accelerates deuterium ions onto a target material which is impregnated with tritium. The deuterium ions are supplied from a replenisher which comprises a material impregnated with deuterium which is boiled off by heating. The deuterium atoms thus provided are then supplied to an ion source comprising a region of the tube in which electric fields are provided to ionize the atomic deuterium from the replenisher and to focus the positive ions into a beam suitable for acceleration onto the target material. The target material is generally kept at a high negative potential. The ion source is provided with an electrode structure which may be regarded as somewhat analogous to that of a conventional triode vacuum tube and having an element analogous to the control grid of such a tube. By applying a time varying voltage to this control grid element the resultant intensity of neutron output of the accelerator tube may be modulated as a function of time. In this manner a harmonically or sinusoidally alternating intensity neutron output may be produced. For a more detailed description of the methods employed to produce an intensity modulated fast neutron flux as a function of time, reference may be had to the paper entitled "The Generation of Neutron Pulses and Modulated Neutrons Fluxed with Sealed Off Neutron Tubes" by C. W. Elenga and O. Reifenscheweiler, published in the Proceedings of the Symposium on Pulsed Neutron Research, Volume II, pages 609-622, 10th-14th of May, 1965, published by the International Atomic Energy Agency of Vienna, Austria. This paper describes in detail techniques which may be utilized to provide a smoothly modulated neutron flux from a tube of the deuterium-tritium accelerator type as a function of time. Other wave shapes than purely harmonic or sinusoidal modulation may be produced also using these techniques.

For a clearer understanding of the present invention it will be helpful to consider first an explanation of its underlying principles. In this explanation certain simplifying assumptions are made for ease of analysis. For example, it is assumed that a spatially distributed source of thermal neutrons (or a thermal neutron cloud) is created in the earth formations by the action of the high energy neutron source. Also, it is assumed that the slowing down time T_(AS) for the fast neutrons produced by the deuterium-tritium source is considerably shorter than the thermal neutron decay time T_(a). This assumption is valid, for example, in high porosity fluid saturated sands such as those of interest in oil well logging.

THERMAL NEUTRON LIFETIME MEASUREMENTS

In general in thermal neutron lifetime well logging it is assumed (and also generally experienced) that the thermal neutron population as measured by a detector in the well bore decays with time after a neutron burst or pulse according to the following mathematical expression:

    N(t) = Ae.sup.-.sup.α.sup.t + Be.sup.-.sup.β.sup.5 (3)

In Equation (3), n(t) is the neutron population as measured by an arbitrarily spaced detector as a function of time t, Ae⁻.sup.α^(t) is the neutron population of the formation component as measured by the detector at any time t, and Be⁻.sup.β^(t) is the neutron population of the borehole environment component as measured by the detector at any time t. The constants A and B are the initial thermal neutron densities at time t = 0 in the earth formation (A) and the borehole (B) respectively. The constants α and β are the thermal neutron decay constants of the earth formation (α) and the borehole (β), respectively. This equation is equally valid at each of the two detectors 23 and 26 of FIG. 1 although the constants A and B will, in general, be different for different spaced detectors due to porosity and lithology effects as will be subsequently discussed. Thus the following development of the theory of thermal neutron lifetime measurement is equally valid at each detector of FIG. 1 and either one or both may be used for this purpose as desired.

In making measurements of the thermal neutron population as a function of time it will be recognized by those skilled in the art that the detectors 23 and 26 of FIG. 1 could be either thermal neutron detectors (such as helium 3 or boron trifluoride detectors) or could be gamma ray detectors such as the previously described sodium or cesium iodide thallium activated crystals. If thermal neutron detectors, such as the helium 3 or boron trifluoride detectors are used, then the thermal neutrons are measured directly. If sodium iodide thallium activated crystal detectors are used, then gamma rays resulting from the capture of thermal neutrons are detected. This provides an indirect, but proportional, measurement of the number of thermal neutrons present. In either event the thermal neutron population at each detector may be determined as a function of time by counting the number of electrical pulses produced by the detector.

Equation (3) may be Fourier transformed from the time domain into the frequency domain and may be rewritten in the frequency domain as: ##EQU1## In Equation (4), N (ω) is the frequency spectrum of N(t) and may be regarded as the neutron population in the frequency (ω) domain. The other symbols A, B, α and β are as previously defined.

Irradiating the earth formation and the borehole environment with a phase coherent source of fast neutrons which is modulated harmonically at an angular frequency (ω), the resulting cloud of thermal neutrons (and/or capture gamma rays as measured by a thermal neutron or gamma ray detector) is also phase coherent and harmonically modulated, but with a phase lag φ relative to the neutron source. The phase lag is a function of the excitation frequency ω, the decay constants α and β of the earth formation and the borehole environment, respectively. It may be shown that the tangent of the phase angle φ is given by the following expression: ##EQU2## where the symbols A, B, α, β, ω, and φ are as previously defined.

Equation (5) may be simplified by making the substitutions B/A = R (i.e., R is representative of the ratio of the borehole component thermal neutron density to the earth formation component thermal neutron density at the detector) and Tan φ/ω = X resulting in: ##EQU3##

Equation (6) contains the three unknown parameters required to determine the earth formation thermal neutron decay constant α (the reciprocal of the thermal neutron decay time), the borehole thermal decay constant β, and the ratio of amplitudes of formation and borehole thermal neutron components R. The variable α is the most desirable one of these parameters to obtain knowledge of. It is an indication (i.e., the reciprocal) of the formation thermal neutron decay time which, as has been previously discussed, is very important in determining the possible hydrocarbon content and water saturation of earth formations in the vicinity of a well bore. Since Equation (6) contains three unknowns R, α, and β, at least three independent equations are needed to determine these three unknowns. The three independent equations for determining the three unknowns R, α, and β may be obtained by independently measuring the phase shifts φ, φ₂, and φ₃ at three different modulation frequencies ω₁, ω₂, and ω₃. Assuming that relative phase angle measurements are made at three different modulation frequencies ω₁, ω₂, and ω₃, three equations of the form of Equation (6) are obtained. Combining two of these equations, the unknown variable R may be eliminated resulting in: ##EQU4## where x₁ = Tan φ₁ /ω₁ and x₂ = Tanφ₂ /ω₂.

Equation (7) may be rewriten in the following form as a cubic equation in the unknown α(earth formation thermal neutron decay constant).

    a.sub.3 α.sup.3 + a.sub.2 α.sup.2 + a.sub.1 α + a.sub.0 = 0                                                         (8)

In Equation (8) the ccoefficients a₁ are functions of β, X₁, X₂, ω₁ and ω₂ which are given by the following set of equations:

    a.sub.3 = β.sup.2 (X.sub.2 -X.sub.1)+β(ω.sub.2.sup.2 -ω.sub.1.sup.2)X.sub.1 X.sub.2 +(ω.sub.2.sup.2 X.sub.2 -ω.sub.1.sup.2 X.sub.1)

    a.sub.2 =β.sup.3 (X.sub.1 -X.sub.2)+β(ω.sub.2.sup.2 X.sub.1 -ω.sub.1.sup.2 X.sub.2)+(ω.sub.2.sup.2 -ω.sub.1.sup.2)

    a.sub.1 =β.sup.3 (ω.sub.1.sup.2 -ω.sub.2.sup.2)X.sub.1 X.sub.2 +β.sup.2 (ω.sub.1.sup.2 X.sub.2 -ω.sub.2.sup.2 X.sub.1)+(X.sub.2 -X.sub.1)ω.sub.1.sup.2 ω.sub.2.sup.2

    a.sub.o =β.sup.3 (ω.sub.1.sup.2 X.sub.1 +ω.sub.2.sup.2 X.sub.2)+β.sup.2 (ω.sub.1.sup.2 -ω.sub.2.sup.2)+β(X.sub.1 -X.sub.2)ω.sub.1.sup.2 ω.sub.2.sup.2                                       (9)

similarly measurements may be made at frequencies ω₁ and ω₃ and combined in Equation (7) yield:

    b.sub.3 α.sup.3 + b.sub.2 α.sup.2 + b.sub.1 α +b.sub.0 = 0                                                         (10)

Here the b_(i) are functions of β, X₁, X₃, ω₁, and ω₃ similar to the expressions given in Equations (9) but substituting X₃ for X₂ and ω₃ for ω₂ in Equa. (9). X₃ of course equals Tan φ₃ /ω₃. Equation (10) may also be written in another form as Equation (11):

    C.sub.3 β.sup.3 + C.sub.2 β.sup.2 + C.sub.1β + C.sub.0 = 0 (11)

where the c_(i) are functions of α, X₃, ω₁ and ω₃. Equations (8) and (11) represent two independent equations with β and α as the unknowns. These equations may be solved for α and β, the quantities of interest in neutron lifetime logging, by using certain graphical techniques to be described.

The three different frequencies of intensity modulation of the neutron source chosen for use in the present invention are 400 Hertz, 2000 Hertz, and 4000 Hertz. It will be appreciated by those skilled in the art that frequencies other than these may be used if desired without compromising the inventive concepts. However, these frequencies are suitable for the purposes of this description.

Referring now to FIG. 5, a family of curves is shown which plots -Tanφ₄₀₀₀ versus -Tanφ₄₀₀ for various values of R (shown on the graph) and with β = 50 microseconds (here β = 1/β). These values were calculated from Equation (5) using neutron source modulation frequencies (f = ω/2π) 400 and 4000 Hertz, respectively. FIG. 5a is an expansion of the region of FIG. 5 near the origin in which β is greater than or equal to α(here α = 1/α and β = 1/β). It will be observed that values of α and R may be obtained for the assumed value of β from the graphs of FIGS. 5 and 5a if the two tangent values are measured.

FIG. 4 similarly is a second family of curves wherein -Tanφ₄₀₀ is plotted against -Tanφ₂₀₀₀ for various values of R (shown on the graph) and α with β = 50 microseconds. Again, these values were computed from Equation (5) at the respective frequencies. FIG. 4a is an expansion of the curves of FIG. 4 in the vicinity near the origin where β is greater than or equal to α. Here again if the tangent measurements at the two frequencies are made R and αmay be determined for the assumed value of β.

If we assume for the present that the borehole has β = 50 microseconds, then by measuring -Tan φ at two frequencies the α(true) (true decay time of the formation) may be determined by comparing the measurements of these values of -Tan φ at the two frequencies and using either the graphical representation of FIG. 4 or FIG. 5 for this purpose. Similarly, if the borehole component decay time is known, then other figures similar to either FIGS. 4 or 5 could be used to measure this α(true) of the formation by using these graphical representations at whichever pair of frequencies is desired (i.e., 400-2000 or 400-4000). Using FIGS. 4 or 5 for known β, R can be measured for the different frequency pairs.

However, in field operations β is in general not known and can even vary within a given well depending upon the condition of the borehole fluid, the borehole diameter, the cement thickness or casing size. In this more realistic situation it is necessary to utilize three frequency measurements. In this case both α (true) and β (true) may be determined in the following manner. R(true) may also be determined in this process. First, the charts of FIGS. 4 and 5 are utilized to determine an apparent α, from each of the two pairs of different frequency phase angle determinations (i.e., the α apparent from the 400-2000 Hertz combination, and the α apparent with the 400-4000 Hertz modulation frequencies). Then the spine and ribs plot of FIG. 6 is utilized to derive α (true). Similarly by using FIGS. 4 and 5, values of R apparent may be obtained for assumed β. Then by using the spine and ribs plot of FIG. 11, R (true) may be obtained. In FIG. 6 the value of α apparent at each of these frequency combinations is plotted. The α (true) is then determined from the location of the point on the graphical representation of FIG. 6 which provides a unique solution for α (true) regardless of the value of R and β. Once the α (true) value is determined in this fashion, α may be obtained by substituting the α (true) value back into Equation (7) and solving this equation for β. Similarly, once the two values of R apparent at the assumed β are obtained from FIGS. 4 and 5, FIG. 11 is consulted to derive a unique value for R (true).

The use of this graphical technique for determining α,β, and R can be more readily understood by an illustration of a hypothetical example.

Assume that the following value of the phase shift tangents at the three frequencies have been measured: -Tanφ₄₀₀ = 0.565, -Tanφ₄₀₀₀ = 1.712, and -Tanφ₂₀₀₀ = 1.410. These data points have been plotted in FIGS,. 4, 5, 6, and 11 as illustrated (labeled "EXAMPLE" therein). It may be seen that these values for the phase shift angles indicate α (true) value of 275 microseconds. Similarly, referring to FIG. 11, R (true) is indicated to be 1.6. This value is substituted in Equation (7) yielding α = 50 microseconds. The value of α (true) may be checked by computing -Tan₄₀₀₀ and -Tan₂₀₀₀ using Equation (5) with β = 50 microseconds, and setting R = 1.6. Comparing the calculated -Tanφ values therefrom with the corresponding hypothetical values which were given in the example shows that the above-described measurement procedure is selfconsistent and yields a unique solution for the α (true) and R (true) of the formation.

While the above description of the solution of the foregoing equations for the true formation decay time, α (true) and R (true) have been expressed in terms of graphical solutions performed by use of the graphs of FIGS. 4, 5, 6, and 11 it will be appreciated by those skilled in the art that these graphical representations could be utilized within a properly programmed digital computer located either at the well site in which the measurements are made, or in a remote locations, if desired. A small general purpose digital computer such as the model PDP-11 made by the Digital Equipment Corporation of Cambridge, Massachusetts, could be suitable for this purpose. The graphical representations corresponding to FIGS. 4, 5, 6, and 11 may be entered in the memory of such a digital computer in the form of tables. Appropriate interpolation techniques may be utilized to reach the combination of graphical solutions just described with respect to FIGS. 4, 5, 6, and 11. Thus, it is seen if a well logging tool which can measure the values of the tangent of the phase shift φ at each of three chosen frequencies of intensity modulation of the neutron source is provided, that these measurements of the phase angle tangent values at either or both of the two spaced detectors 23 and 26 of FIG. 1 may then be appropriately combined to derive the true formation and borehole thermal neutron decay time parameters of interest. It is, of course, well known in the art that once the true formation and borehole thermal neutron decay time parameters are known, then appropriate techniques which are known in the art may be applied to derive the formation water saturation (and hence the oil saturation of the formation, providing the porosity is also known).

POROSITY MEASUREMENT

Recalling Equation (4) previously given which defines the thermal neutron propulation N(ω) at a detector in the frequency, ω; domain, it may be shown that the instantaneous count rate C(t) at such a detector may be written as a function of time as (for sinusoidal modulation of the neutron source) :

    C(t) = C.sub.0 + K. |N (ω)|. Sin (ωt + φ) (12)

where

C_(o) = average count rate over a full period T = 2π/ω of modulation

K = a tool constant containing, inter alia, detector efficiency

φ = phase shift at the detector. Since |N (ω)| does not depend on time t, C (t) may be integrated over the first half period T, yielding ##EQU5## Integrating C(t) over the second half of period T yields a similar expression ##EQU6## Subtracting Equation (14) from Equation (13) yields

    C .sub.1/2 - C .sub.2/2 = 4.|N(ω)|.K (15)

if, as will be discussed in more detail subsequently, the counts at each of the two detectors are counted and accumulated over quadrant intervals of each period of modulation (T/4 in duration) and are labeled C₁ for the first quandrant, C₂ for the second quandrant, C₃ for the third quandrant and C₄ for the fourth quandrant, then Equation (15) may be written as:

    C.sub.1/2 - C.sub.2/2 = (C.sub.1 +C.sub. 2)-(C.sub.3 +C.sub.4) (16)

it will be recalled that Equation (4) defines the thermal neutron population N(ω) in the frequency domain in terms of a borehole component amplitude β and a formation component amplitude A at a detector. However, in the previous section it has been shown that the ratio R (true) = B/A may be derived independently by the use of the three frequency modulation technique at a detector. Similarly, this technique can be used to obtain α (true) and β (true) at the detector in question. Using the substitution R = B/A. then Equation (4) may be rewritten as follows: ##EQU7## It will be observed that if α, β, and R are considered as known parameters from the technique of the previous section, that according to Equation (17) the counts accumulated at a detector according to Equations (15) and (16) are directly proportional to the amplitude A, of the formation component of the total gamma radiation at the detector.

Now, if such an accumulation of counts according to Equation (15) and (16) is made at each of two detectors, the amplitude Ai i = 1,2 of the formation component of gamma radiation at each detector will in general, be different and will in general be, as will be shown subsequently, dependent on the slowing down length L_(b) for the fast (14 MEV) neutrons emitted by the source. The slowing down length L_(b) may, in turn, be related to (as will be shown) the porosity Φ of the earth formations in the vicinity of the tool. Thus, the ratio of the amplitudes A1/A2 of the formation components of gamma radiation accumulated according to Equations (15) and (16) at the two different spaced detectors may be written as: ##EQU8## It will be observed that all quantities on the right hand side of Equation (18) are known or measured.

From the theory of neutron slowing, and more particularly, from the theory of the diffusion of fast neutrons in a porous medium, it may be shown that the neutron flux F(d) at a distance d from the source is given by: ##EQU9## where Q is the source strength

D is the thermal neutron diffusion coefficient

L_(a) is the thermal neutron diffusion length, and

L_(b) is the slowing down length. For earth formations usually encountered in borehole logging L_(b) > L_(a). For example, consider salt water filled sandstone formations at typical porosity Φ values as shown in Table I:

                  TABLE I                                                          ______________________________________                                         Φ       L.sub.b (cm.)  L.sub.a (cm.)                                       ______________________________________                                         15          12.0           7.2                                                 30          9.6            4.6                                                 ______________________________________                                    

So, if d ≧ 60 cm., then F (d) can be approximated to a high degree of accuracy as ##EQU10##

For a well logging sonde having two detectors such as detectors 23 and 26 of FIG. 1 spaced d₁ and d₂ from the source where d₁ < d₂ and d₁ > 60 cm., the ratio of neutron flux at the detector is given by ##EQU11##

It should be noted that source to detector spacings greater than 60 cm. are feasible using the sinusoidally modulated neutron source of the present invention, where using pulsed sources (square wave) as in the prior art such spacings would typically produce too low counting rates to be practical.

Using the relationships of Equations (21) and (18) and recalling that F(d) is proportional to the thermal neutron capture gamma radiation detected at a detector, it can be seen that ##EQU12##

It will be noted that Equation (22) is independent of the thermal neutron parameters L_(a) and D. This is a distinct advantage over prior art porosity measuring techniques since L_(b) is primarily dependent on the amount of hydrogen present in the formation, which is in turn, related to the formation porosity Φ . On the other hand L_(a) and D are strongly dependent on salinity, boron content (shaliness) and lithology characteristics of the formation. Thus, the present porosity measurement technique can provide a more accurate and reliable indication of porosity than prior art neutron porosity measurement techniques.

Solving Equation (22) for L_(b), the neutron slowing down length is given by ##EQU13## where all quantities on the right hand side are known. Referring now to FIG. 10 a graphical plot of L_(b) is given as a function of porosity Φ for several fluid and lithology combinations. If L_(b) is thus determined from Equation (23) the graphical representation of FIG. 10 may be used to obtain the porosity Φ very accurately provided only the general nature of the lithology (such as sandy or limestone) is known independently as from a density log or sonic log.

Summarizing, the porosity detection technique of the present invention using the dual spaced detectors and the three frequency modulation is as follows:

1. The α, β, and R true values are determined as outlined in the previous section.

2. Simultaneously with this first step the count rate combinations in the four quadrant intervals as given by Equation (16) are formed for each of the detectors.

3. The formation component amplitude ratio at each detector Z of Equation (22) is then formed by use of Equation (18) and the appropriate αi, βi, Ri i = 1,2 and detector count rates C_(1i), C_(2i), C_(3i), and C_(4i).

4. The neutron slowing down length is then obtained from Equation (23) and used in conjunction with FIG. 10 to obtain the porosity Φ .

DESCRIPTION OF SYSTEM ELECTRONICS

Referring now to FIGS. 2 and 3 the well logging system shown schematically in FIG. 1 is illustrated in more detail. Considering first the circuitry of the downhole portion of the system in FIG. 2, it will be seen that two gamma ray detectors 101 and 102 comprising (as illustrated) thallium doped sodium or cesium iodide crystals is optically coupled to photomultiplier tubes which produce electrical pulses proportional in height to the energy of the gamma ray impinging upon the detectors 101 and 102. The electrical pulse signals from the detectors 101 and 102 are amplified and supplied therefrom to pulse height discriminators 103 and 104. Discriminators 103 and 104 are used to discriminate against relatively low energy background gamma radiation and each has an adjustable discriminator level as indicated by potentiometer 105. This level is usually set at about 0.5 MEV, so that most gamma rays resulting from naturally occurring background radiation may be discriminated against. The output data pulses from the pulse height discriminators 103 and 104 are supplied via line 106 to three AND gates 107, 108, and 109 whose conditioning will be described in more detail subsequently. The output of detector 101 is supplied as positive polarity pulses and the output of detector 102 is supplied as negative polarity pulses via the inverter 103a of FIG. 2.

The transmission of the data pulses to the surface is controlled in synchronization with the operation of the neutron generator tube 110 of FIG. 2. A 16 kilohertz oscillator driver 111 is utilized to generate timing pulses. The 16 kilohertz output pulses from the oscillator 111 are supplied on a line 112 as inputs to a divide by 16,000 divider circuit 113, to a divide by 4 divider circuit 114, to a divide by 8 divider circuit 115, and to a divide by 40 divider circuit 116. As the frequency of the 16 kilohertz oscillator is divided by 16,000 in the divider circuit 113, output pulses are produced by the divider 113 which occur once each second during the operation of the system. The once per second output pulses are provided from divider 113 on line 117 and are used to trigger (via an amplifier 118) the reset of divider circuits 114, 115, and 116 once each second.

The once per second output pulses from the divider 113 are also supplied by to a divide by 3 one shot multivibrator 158 which has multiple outputs comprising lines 119, 120, and 121. Divide by 3 one shot circuit 158 functions, upon the receipt of a pulse on its input line 117, to produce a voltage level output on line 119 for a one second duration beginning upon receipt of the first such pulse on its input line 117. Upon receipt of its second input pulse on line 117 (at the end of one second of operation) the output voltage level is removed from line 119 and applied to line 120. Similarly at the end of the second one second of operation, the third input pulse is received on input lead 117, divide by 3 one shot 158 produces an output voltage level of one second duration on line 121. Upon receipt of the fourth one second input pulse on line 117 the output voltage level is removed from line 121 and restored to line 119. Thus, the divide by 3 one shot 158 provides successive conditioning voltage levels on output lines 119, 120, and 121 which are used to condition successively three AND gates 122, 123, and 124.

Considering now the generation of a 400 Hertz sine wave modulation which is to be applied to the neutron generator 110, this is accomplished in the following manner. Input pulses on line 112 to divide by 40 multivibrator 116, which it will be recalled is reset at the beginning of each second by output pulses from divide by 16,000 circuit 113, produces a 400 Hertz square wave output from divider 116 on output line 125. This signal is supplied as one input to AND gate 122, during the first second of operation of a three second cycle of operation of the apparatus. The AND gate 122 is conditioned to pass the 400 Hertz square wave pulses supplied on input line 125 during the initial second of the three second operational cycle. The 400 Hertz square wave pulses passed by the AND gate 122 are thus supplied during this initial second of operation to a 400 Hertz band pass filter 126 which shapes the square wave pulses into a sine wave shape by the action of the tuned circuitry contained therein. Thus, the output of the 400 Hertz band pass filter 126 comprises a 400 Hertz sine wave which is supplied as input to an amplifier 127 and amplified to a more usable signal level. This signal is supplied as input to a driver amplifier 128 which is coupled to the neutron generator tube ion source and thus applied as a sine wave intensity modulation to the neutron flux output of the generator tube.

The AND gates 123 and 124 are similarly conditioned during the second and third seconds of a three second operational cycle of the apparatus. The two kilohertz square wave output of divide by 8 circuit 115 is supplied on input line 129 to AND gate 123. The four kilohertz square wave output pulses from divide by 4 circuit 114 are supplied on input line 130 to AND gate 124. Outputs from AND gates 123 and 124 are similarly shaped by 2000 Hertz band pass filter 131 and 4000 Hertz band pass filter 132 to provide sine wave output wave shapes to amplifiers 133 and 134 respectively during the second and third seconds of the operational cycle of the circuit. In this manner, an intensity modulated neutron output at 400 Hertz for the first second of operation, 2000 Hertz for the second second of operation and 4000 Hertz for the third second of operation are provided. This modulation cycle is depicted graphically in FIG. 8 of the drawings.

Now concerning the synchronization of the transmission of the detected gamma rays during the different intervals of neutron modulation for transmission to the surface, it will be observed that the output conditioning signals from divide by 3 one shot 158 are supplied on lines 119, 120, and 121 to AND gates 107, 108, 109, 135, 136, and 137. It will be recalled that date pulses from the detectors 101 and 102 are continuously coupled to one input of AND gates 107, 108, and 109. Similarly, 16 kilohertz clock pulses are supplied via pulse shaper circuit 138 (which may be of conventional design) to the opposite inputs of AND gates 135, 136, and 137. During the first second of operation of a three second operating cycle the AND gate 109 and the AND gate 137 are conditioned for operation while the remaining AND gates 107, 108, 135, and 136 are in a blocked condition. Thus, during the first second of operation data pulses from the detectors 101 and 102 are passed by AND gate 109 and the AND gate 137 passes the 16 kilohertz clock pulses. These pulses are supplied with the clock pulses being of negative polarity. The data pulses are of mixed polarity as described depending on which detector they are from. Inverter amplifiers 140, 141, and 142 reverse the polarity of the clock pulses and amplify them to a much higher signal level than that of the data pulses. The data pulses and the clock pulses are summed at mixing point 143 during the first second of operation. The large amplitude negative polarity clock pulses and data pulses of mixed polarity are then linearly amplified by a predetermined scale factor by amplifier 144 during this first second of operation of a three second cycle of the neutron source which is being modulated at a 400 Hertz frequency. The data pulses detected during this portion of the cycle and the clock pulses from the 16 kilohertz clock oscillator 111 are applied to a pulse transmission circuit 145 for transmission to the surface. Similarly, during the second second of operation mixed polarity data pulses from the detector system are supplied together with the large amplitude negative polarity 16 kilohertz clock pulses via a second scale factor amplifier 146 to the pulse transmission circuit 145 for transmission to the surface. Finally, during the third second of the three second operating cycle, mixed polarity data pulses and large amplitude negative polarity clock pulses are supplied to the pulse transmission circuit 145 via a third scale factor amplifier 147. The amplification levels of the scale factor amplifiers 144, 146, and 147 are set substantially apart so that at the surface, the signals representing the clock pulses and the data pulses occurring during the three different time gating intervals may be separated from each other by the use of a pulse height discriminator as will be described. That is to say, the scale factor amplifier 144 may have a gain factor of 10 while the scale factor amplifier 146 may have a gain factor of 20 and the scale factor amplifier 147 may have a gain factor of 30. Thus, during the three different seconds of the operational cycle, signal levels transmitted to the pulse transmission circuit 145 have substantially different voltage levels prior to their introduction to the cable for transmission to the surface. This transmission scheme is depicted graphically in FIG. 7.

Output signals from the pulse transmission circuit 145 are capacitively coupled via a capacitor 153 to the center conductor 152 of the well logging cable. High voltage D.C. for the operation of the photomultiplier tubes in detectors 101 and 102 is also provided on the center conductor of this cable from surface power supplies. The B+ voltage for operation of the preamplifier portions of detectors 101 and 102 is supplied from a surface power supply on the shield 151 of this cable. Thus, a signal wave form as illustrated in FIG. 7 is applied to the cable during the operation of the downhole equipment. In the illustration of FIG. 7 the first second of operation (illustrated at 201) is characterized by the transmission of large amplitude negative sharp spike synchronization pulses and smaller amplitude mixed polarity data pulses occurring at a random interval following each of the 16 kilohertz synchronization or clock pulses. Similarly, during the second second of operation (202 of FIG. 7) the large amplitude negative sharp spike synchronization pulses occur, but with a larger voltage amplitude than during the first second of operation. The randomly occurring mixed polarity data pulses again have a positive voltage and follow each sync pulse. Finally, during the third second of operation (as illustrated at 203 in FIG. 7) the negative large amplitude 16 kilohertz clock pulses occur at regularly spaced intervals. Each sync pulse is followed by plurality of randomly occurring mixed polarity pulses corresponding to gamma ray counts made during the intervals between the 16 kilohertz data pulses.

This information is transmitted to the surface where it is interpreted in terms of the tangents of the phase angles occurring at each of the three different modulation frequencies by the data processing circuitry shown in FIG. 3. Prior to the consideration of the operation of the circuitry of FIG. 3, however, it will be appropriate to consider how the tangent of the phase angle is determined. Referring to the drawing of FIG. 9 a single cycle of the intensity modulated neutron cloud at the neutron source (solid curve) and at the neutron detector (dashed curve) is illustrated schematically. The straight line (labeled N(avg)) represents the average neutron population generated. It will be observed that a phase shift between the neutron population at the source and at the detector due to the neutron lifetime (or thermal neutron decay time) of the borehold and formation materials, exists as previously discussed. If the neutron source modulation cycle begins at t_(o) as shown, and is divided into four quadrants as a function of time, these quadrants will end at t₁, t₂, t₃, and t₄ and will each be of a duration t₁ - t_(o) which is dependent on the modulation frequency ω. If the counts of capture gamma rays occurring at the detector during each of the four quadrants of the modulation cycle are labeled C₁, C₂, C₃, and C₄, then it may be shown that the tangent of the phase angle φ is given by: ##EQU14##

Thus, it is possible by determining the counts of gamma rays occurring in each of the four quadrants of a cycle of modulation of the fast neutron source, to derive the relative phase angle φ of the phase coherent neutron cloud at the detector with respect to the modulated cloud of thermalized neutrons produced by the fast neutron source. The only approximation used in making this derivation of the tangent of the phase angle is that the slowing down time of the fast neutrons is short with respect to the thermal neutron decay time (or neutron lifetime) of the earth formation in the vicinity of the well borehole. This is usually an excellent approximation. Similarly counts C₁, C₂, C₃, and C₄ are used in the porosity determination as previously discussed. It will be noted in this respect that the denominator of the expression for Tan φ in Equation (24) is the same expression (i.e., (C₁ + C₂) - (C₃ + C₄)) which is required in the determination of the ratio A1/A2 of Equation (18). This fact will be exploited.

Referring now to FIG. 3, the surface data processing signal equipment is illustrated in block diagram form. The well logging cable 150 center conductor 304 is provided with high voltage for the operation of the photomultiplier tube (102 of FIG. 2) by high voltage power supply 305 which is resistively coupled thereto by resistor 303. The B+ voltage for the operation of associated downhole circuits is coupled from B+ power supply 383 to the inner coaxial shield of the logging cable 150 in a similar manner. The alternating current data signals produced by the downhole equipment are extracted via a coupling capacitor 302 and supplied as input to a pulse separator 306. It will be recalled that the 16 kilohertz synchronization pulses are provided as large amplitude negative going voltages on this cable while the data pulses are provided as randomly occurring smaller amplitude mixed polarity pulses. The sync pulse separator 306 functions to provide output pulses on three lines with the large amplitude 16 kilohertz synchronization pulses occurring on output lines 307 and 307a and the randomly occurring smaller amplitude mixed polarity data pulses on output line 308. The mixed polarity data pulses are separated further on the basis of polarity by detector separator 306a. The data pulses for detector No. 1 are output on line 308a to the detector No. 1 processing circuit shown in the dotted box. The detector No. 2 data are supplied on line 308 to detector No. 2 circuit 306b. As the detector No. 1 and detector No. 2 processing circuits are almost exactly the same, it will suffice herein to describe only the detector No. 1 processing circuit in detail.

It will be recalled that the three different frequency portions of modulation of the downhole neutron generator were characterized by the three different levels of voltage amplifications which are applied to both the synchronization pulses and clock pulses at the downhole tool. This results in three different voltage amplitude components which correspond to the three different frequency modes of operation being supplied to the surface equipment. Thus, the output synchronization pulses on line 307 (as illustrated in FIG. 7) occur at three different characteristic voltage levels when output from the sync separator 306. These synchronization pulses are input to three voltage level discriminators 309, 310, and 311. Voltage level discriminators 309 310, and 311 separate the clock pulses which occur during each period of one second duration of the different frequency modulations applied to the downhole neutron source on the basis of their different amplitudes. Voltage level discriminator 309 thus permits only clock pulses occurring during the 400 Hertz modulation to be output therefrom on line 312. Similarly, 2000 Hertz voltage discriminator 310 only permits synchronization or clock pulses to be output therefrom on line 313, while 4000 Hertz voltage discriminator 311 only permits clock pulses to be output therefrom on line 314 during the 4000 Hertz modulation.

Voltage level discriminators 309, 310, and 311 thus provide clock or sync pulse output on their respective output lines 312, 313, and 314 only while their respective modulation frequency periods are occurring in the downhole tool. Considering now the operation of the portion of the circuitry which concerns the 400 Hertz intensity modulation of the downhole neutron source, the occurrence of the clock or sync pulses on line 312 (which is permitted to enter at the beginning of the 400 Hertz modulation) is used to set (after a 2.5 millisecond delay provided by a delay divide by 40 circuit 380) a flip-flop 315 and to immediately reset a second flip-flop 316 in the 4000 Hertz modulation portion of the circuit. Similarly, the occurrence of the clock pulses on output line 313 is used to set (after a 2.5 millisecond delay provided by delay divide by 40 circuit 381) a flip-flop 317 and to immediately reset the flip-flop 315. This action causes the three channels of the circuit (corresponding to the three different frequencies of modulation) to be alternately and singly activated for counting purposes as the voltage level on the output lines of flip-flops 315, 316, and 317 are used to condition a plurality of AND gates and will be described subsequently. The 2.5 millisecond delays provided by delay circuits 380, 381 and 382 are included to allow any phase shift effects of thermal neutrons from the just completed different modulation frequency portion of the operating cycle to die away before beginning to make the phase shift determination at the new operating frequency. A few counts will be lost in this manner (only about 0.25 percent) but increased accuracy will result. The 2.5 millisecond delay is one full period of 400 Hertz modulation, five periods of 2000 Hertz modulation and 10 periods of 4000 Hertz modulation. These times far exceed the amount of phase shift to be measured and will allow effects from the previous modulation cycle to dissipate prior to the beginning of measurement.

Returning now to the consideration of the 400 Hertz modulation processing circuitry, the clock pulses occurring on line 312 are supplied as input to a countershift register 318 during a 400 Hertz modulation of the downhole neutron source. One complete cycle of modulation of the source occurs each one four-hundredth of a second (2500 microseconds). The clock pulses at 16 kilohertz appear once each 62.5 microseconds. Thus, upon the occurrence of each ten clock pulses supplied to the counter shift register 318, one quadrant of one cycle of modulation of the downhole neutron source occurs. Countershift register 318 provides an output voltage level on line 319 during the first quadrant of one cycle of modulation; it provides an output voltage level on line 320 during the second quadrant of such cycle of modulation; it provides an output on line 321 during the third quadrant of the cycle of modulation; and it provides an output voltage level on line 322 during the fourth quadrant of the cycle of modulation. These output voltage levels provided successively on lines 319, 320, 321 and 322 are also used in conditioning the plurality of AND gates associated with this circuitry. It should be mentioned here that the counter-shift register 318 is also reset by the appearance of the first clock pulse appearing on output line 313 from the 2000 Hertz voltage level discriminator 310, so that upon completion of one second of the 400 Hertz modulation, the first clock pulse appearing on output line 313 clears the counter-shift register 318 circuit and enables it to start counting anew upon the initialization of the next 400 Hertz modulation portion of the operational cycle of the downhole equipment.

The AND gates 323, 324, 325 and 326 are associated with the 400 Hertz channel of the circuit of FIG. 3. These multiple input AND gates require the presence of a voltage level on each of their three input leads before they will produce a pulse. One input lead of each of AND gates 323, 324, 325 and 326 is connected to the gamma ray count data input line 308 from the pulse separator circuit 306. A second input lead of each of these AND gates is connected to the conditioning flip-flop 315 described previously, and the third input lead of each of these multiple input AND gates is connected to one of the output lines of counter-shift register 318, which corresponds to one of the quadrants of a cycle of modulation of the downhole neutron source. Thus, during the first quadrant of operation of a 400 Hertz modulation cycle in the downhole tool (following the 2.5 millisecond delay), data pulses are permitted only through AND gate 323. Similarly, during the second quadrant of a 400 Hertz modulation cycle the data pulses are only permitted through AND gate 324 and, similarly, AND gates 325 and 326 permit the passage of data pulses occurring only during the third quadrant and fourth quadrant respectively of a cycle of 400 Hertz modulation. Four OR gates 327, 328, 329, and 330 together with a pair of up/down counters 331 and 332 are used to form the expressions of the numerator and denominator of the fraction of Equation (12) in the following manner.

C₁ counts occurring during the first quadrant of the modulation cycle from AND gate 323 are supplied as inputs to OR gates 327 and 329. Similarly C₂, second quadrant, outputs from AND gate 324 are supplied as inputs to OR gates 328 and 329. C₃ counts occurring during the third quadrant of the 400 Hertz modulation cycles are supplied as inputs to OR gates 328 and 330. Finally, during the fourth quadrant of modulation, C₄ counts are supplied to OR gates 330 and 327. The numerator of the fraction of Equation (24) is formed in up/down counter 331 while the denominator of this expression is formed in up/down counter 332. Observing the numerator of the fraction of the expression of Equation (24) it will be noticed that the expression may be formed by counting up during quadrants 1 and 4 in counter 331 and counting down (subtracting) during quadrants 2 and 3 in the same counter. Thus, the C₂ and C₃ counts are supplied to the down count input terminal of up/down counter 331 while the C₁ and C.sub. 4 counts are supplied to the up/count input terminal in this counter. Thus, at the end of each complete cycle of 400 Hertz modulation of the neutron source the up/down counter 331 contains a digital number representative of the numerator of the fraction of the expression of Equation (24).

Similarly, the expression of the denominator of the fraction of Equation (24) is formed during each cycle of modulation in the up/down counter 332. Thus during the one-second 400 Hertz modulation period of a given operational sequence in the downhole tool, up/down counters 331 and 332 contain the expressions representing the numerator and denominator of the fraction of Equation (24). It will be recalled that the denominator of Equation (24) term will also be used in forming the ratio A₁ /A₂ of amplitudes at each detector at each frequency of Equation (18) which is used in the porosity determination.

Now concerning the extraction of these digital numbers contained in counters 331 and 332, the plurality of one shot and delay one shot multivibrators 333 - 341 is used for this purpose. Upon the occurrence of an output voltage level from the flip-flop 315, a voltage is applied on line 342 to a delay one shot 336 and to a transfer one shot 333. The occurrence of a voltage pulse on one shot 333 causes and X' transfer voltage to be output from one shot which is supplied to quad latch circuits 343 and 344. This causes the quad latch circuits 343 and 344 to extract the digital number contained in the up/down counters 331 and 332 at that time. The presentation of this voltage level on line 342 to the delay one shot 336 causes the occurrence (at a time one second later) of an output voltage from the delay one shot 336 which is input to a one shot multivibrator 339. Multivibrator 339, in turn, provides an output X voltage for resetting the up/down counters 331, 332.

The result of the X transfer one shot voltage levels and the X' reset voltage levels is to cause the output of up/down counters 331 and 332 to be extracted at the end of each one second period of 400 Hertz modulation of the neutron source and the up/down counters forming the numerator and denominator of the fraction of Equation (24) to be reset following each one second period of operation at the 400 Hertz frequency of modulation in the downhole tool. In a similar manner, one shots 334 and 337 are responsive to input voltages on lines 350 and 351 corresponding to the occurrence of output clock pulses from flip-flops 317 and 316, respectively and cause the extraction into quad latch circuits 352, 353, 354 and 355 of the numerator and denominator signals accumulated in a similar manner in the up/down counters 356, 357, 358 and 359 of the circuits corresponding to the 2000 Hertz and 4000 Hertz modulation portions of the operative cycle of the downhole tool.

Returning to consideration of the 400 Hertz modulation channel, the digital numbers occurring at the end of the one second periods of modulation in the quad latches 343 and 344 are then applied to digital to analog converter circuits 360 and 361 which convert these into analog voltage levels are applied to analog ratio circuits 362 and 392 which provide, respectively, an output signal equal to the expression -Tan₄₀₀ (or tangent phase angle at 400 Hertz) and the quadrant count rate ratio at the two spaced detectors i = 1,2 of the expression of Equation (18). In a similar manner, digital to analog converter circuits 363, 364, 365 and 366 provide output voltage levels corresponding to the numerator and denominator of the fractions of the expression of Equation (24) for the other two operating frequencies of 2000 Hertz and 4000 Hertz modulation. These signals are then supplied as inputs to analog ratio circuits 367, 368, 390 and 391 to provide output signals representative of the tangent of the phase angle occurring at each of these frequencies of modulation together with the dual detector amplitude ratio terms of Equation (18) at these frequencies. Thus, analog ratio circuits 362, 367 and 368 provide analog output voltages representative of the tangent of the phase angle occurring at each of the operative modulation frequencies of the downhole neutron source. Analog ratio circuits 390, 391 and 392 provide output voltages representative of the quadrant count rate ratio terms used in evaluating the expression of Equation (18) at each of the three frequencies of operation. These quantities may be supplied to recording channels in the recorder 18 of FIG. 1 for recording as a function of borehole depth. Alternatively they can be supplied to digital computing apparatus, as previously discussed, for computing directly the borehole and formation components of the thermal neutron lifetime together with the slowing down length L_(b) and porosity in the manner previously described.

While only the 400 Hertz channel of the data processing circuit of FIG. 3 has been described in detail, it will be appreciated that the 2000 and 4000 Hertz channels function in an analogous manner. The only differences between these channels occurs in the timing of the four sequential outputs of counter shift registers 369 and 370 which occur at times appropriate to delineate quadrant counts at each of these modulation frequencies appropriately. Similarly the circuits of Detector No. 2 processing circuit 306b of FIG. 3 are analogous to the just described circuits of Detector No. 1 processing circuit, and hence need not be detailed further.

The foregoing descriptions may make other alternative embodiments in accordance with the concepts of the present invention apparent to those skilled in the art. It is therefore the aim of the appended claims to cover all such changes and modifications as fall within the true spirit and scope of the invention. 

I claim:
 1. A method for simultaneously determining the thermal neutron decay time and the porosity of earth formations in the vicinity of a well borehole comprising the steps of:continuously irradiating the earth formations in the vicinity of a well borehole with a phase coherent harmonically intensity modulated cloud of fast neutrons having at least three different frequency modulation components; detecting as a function of time the intensity modulated thermal neutron populations resulting from said irradiation of said at least three different modulation frequencies at least at two different longitudinal distances from the source of said irradiation in the borehole; determining from said detected thermal neutron populations measured as a function of time at said different longitudinal distances from the source of said irradiation, the relative phase shift between said fast neutron cloud and said thermal neutron population at said at least three different modulation frequencies at said different longitudinal distances; combining said three different modulation frequency relative phase shift measurements at least at one of said different longitudinal distances according to a first predetermined relationship to derive an indication of the thermal neutron decay time of the earth formations in the vicinity of a well borehole; and combining said three different modulation frequency relative phase shift measurements at least at two of said different longitudinal distances from the source of said irradiation according to a second predetermined relationship to derive an indication of the porosity of the earth formations in the vicinity of a well borehole.
 2. The method of claim 1 further including the step of:combining said three different modulation frequency relative phase shift measurements at least at one of said different longitudinal distances from the source of said irradiation according to a predetermined relationship to derive an indication of the thermal neutron decay time of the borehole fluid in a well borehole.
 3. The method of claim 1 wherein the step of detecting as a function of time the intensity modulated thermal neutron populations resulting from said irradiations at least at two different longitudinal distances from the source of said irradiation is performed by detecting gamma radiations resulting from the capture of thermal neutrons by the nuclei of materials present in the borehole and its vicinity at said at least two different longitudinal distances.
 4. The method of claim 1 and further including the step of performing said method steps along a borehole as a function of depth and recording said indications of the thermal neutron decay times and said indications of porosity so measured as a function of borehole depth.
 5. The method of claim 2 and further including the step of performing said method steps along a borehole as a function of depth and recording said indications of earth formation thermal neutron decay time, borehole fluid thermal neutron decay time and formation porosity as a function of borehole depth.
 6. The method of claim 1 wherein the step of determining the relative phase shift between said fast neutron cloud and said thermal neutron population at said at least three different modulation frequencies at least at two different longitudinal distances from the source of said irradiation is performed by separating the modulation cycle at each of said at least three different modulation frequencies into at least four equal time intervals corresponding to quadrant cycle intervals at the respective modulation frequency and measuring the thermal neutron populations in such quadrant cycle intervals and combining such measurements at least at one of said different longitudinal distances in a predetermined manner to derive an indication of said relative phase shift.
 7. The method of claim 6 wherein said measurements of the thermal neutron population in said quadrant cycle intervals are combined to derive a measure of the tangent of the relative phase shift between said fast neutron generation and said thermal neutron population at each such modulation frequency.
 8. The method of claim 6 wherein said quadrant cycle measurements are combined according to the relation ##EQU15## where φ is the relative phase shift angle and C₁, C₂, C₃ and C₄ are count signals representative of the thermal neutron population measurements in the first, second, third and fourth quadrants of a modulation cycle respectively.
 9. The method of claim 1 wherein the step of determining said relative phase shift between said fast neutron cloud and said thermal neutron populations at said at least three different modulation frequencies at least at two different longitudinal distances further includes separating the modulation cycle at each modulation frequency into at least four equal time intervals corresponding to quadrant cycle intervals, measuring the thermal neutron populations in said quadrant cycle intervals at each such frequency at each such detecting longitudinal distance and combining such measurements in a predetermined manner to derive an indication of the formation component amplitude of thermal neutron population at each such distance at each such frequency.
 10. The method of claim 9 and further including the step of combining said formation component thermal neutron population indications at each of said at least two different spaced longitudinal distances to derive an indication of the fast neutron slowing down lengths L_(b) in the earth formations in the vicinity of the borehole.
 11. The method of claim 10 and further including the step of determining the earth formation porosity by comparing said fast neutron slowing down lengths in a predetermined manner to derive an indication of the porosity of the earth formation in the vicinity of the borehole.
 12. A method for logging earth formations traversed by a fluid filled well borehole to develop a measurement of thermal neutron interaction characteristics of such formations comprising the steps of:moving a well logging sonde sized and adapted for passage through a well borehole past earth formations penetrated by a well borehole; continuously generating fast neutrons in said sonde and bombarding the surrounding media with such neutrons to develop a thermal neutron population in the borehole and surrounding media; harmonically modulating the intensity of said fast neutrons at, at least three different modulation frequencies; detecting the thermal neutron populations in the vicinity of said sonde at least at two different longitudinal distances from said fast neutron generator as a function of time and developing signals representative thereof; and combining said representative signals according to predetermined relationships to derive an indication of the thermal neutron decay time and the porosity of the earth formations in the vicinity of the borehole.
 13. The method of claim 12 and further including the step of combining said representative signals according to predetermined relationships to simultaneously derive an indication of the thermal neutron decay time of the borehole fluid.
 14. The method of claim 13 and further including the step of recording said indications of the thermal neutron decay time characteristics of the earth formations and the borehole fluid and the porosity as a function of the borehole depth of said sonde.
 15. The method of claim 12 wherein the step of detecting the thermal neutron population as a function of time at least at said two different longitudinal distances from said fast neutron generator is performed by detecting said thermal neutron population during quadrant intervals of a cycle of modulation at each of said at least three different intensity modulation frequencies and generating signals representative thereof.
 16. The method of claim 15 and further including the step of combining said representative quadrant signals in a predetermined manner to derive indications of the relative phase shift between the intensity of the fast neutrons and the thermal neutron population at each of said different frequencies of intensity modulation at each of said at least two different longitudinal distances.
 17. The method of claim 16 wherein said representative quadrant signals are combined to derive an indication of the tangent values of the phase shift angles at each of said different frequencies of intensity modulation at each of said at least two different longitudinal distances.
 18. The method of claim 12 wherein the step of harmonically modulating the intensity of said fast neutrons at, at least three different modulation frequencies is performed by modulating said intensity at a first frequency for a first time interval followed by immediately modulating said intensity at a second frequency for a second time interval followed by immediately modulating said intensity at a third frequency for a third time interval to form a modulation sequence and repetitively repeating this modulation sequence as said sonde is moved through the borehole.
 19. The method of claim 18 wherein said first, second and third time intervals are of equal duration.
 20. The method of claim 18 wherein said step of detecting the thermal neutron population as a function of time is performed by detecting said thermal neutron population during quadrant cycle intervals of said first frequency during said first time interval, detecting the thermal neutron population during quadrant cycle intervals of said second frequency during said second time interval, and detecting the thermal neutron population during quadrant cycle intervals of said third frequency during said third time interval.
 21. The method of claim 20 wherein said first, second and third time intervals are of equal duration.
 22. The method of claim 21 wherein said modulation frequencies are chosen to be 400 Hertz, 2000 Hertz and 4000 Hertz respectively.
 23. The method of claim 20 and further including the step of delaying, for a predetermined duration, at the beginning of each of said first, second and third time intervals the detection of the thermal neutron population to allow phase shift effects from the prior modulation frequency interval to substantially die away and then resuming said detection for the remainder of said time interval.
 24. The method of claim 23 wherein said predetermined delay duration comprises an integral number of modulation cycles of each of said different modulation frequencies. 